Solve for $x$ and $y$ using elimination. $\begin{align*}x-y &= 4 \\ -7x-8y &= 2\end{align*}$
We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $7$ and the bottom equation by $1$ $\begin{align*}7x-7y &= 28\\ -7x-8y &= 2\end{align*}$ Add the top and bottom equations. $-15y = 30$ Divide both sides by $-15$ and reduce as necessary. $y = -2$ Substitute $-2$ for $y$ in the top equation. $x+ 2 = 4$ $x+2 = 4$ $x = 2$ The solution is $\enspace x = 2, \enspace y = -2$.